How can I convert multiple mirror ball exposures into an HDR?
Blender is not the right tool for this job. Not only will you have a hard time getting the functionality you need, but Blender's color management is fundamentally flawed, so even if you do get results, they'll be wrong.

A better tool would be Hugin. It's specifically designed for exactly the kind of thing you're trying to do (creating an HDR/EXR from a set of LDR images). It's free, open-source, and relatively well supported. Your task is smack-dab in the middle of what Hugin was made for, so you shouldn't have any trouble finding (modern) tutorials for that.

EDIT: If you REALLY want to do this in Blender, I'd be interested to see the results if you used them as textures on an emissive plane. If you ADD (not multiply) all the images together (mix node set to add, two images in; that mix node out to another mix node set to add, with another image in; and so on until you've added all the images together), you'll come up with... something. It'll definitely be higher dynamic range... and it'll definitely contain all the data.

Put that texture on an emissive plane, and render that out to an HDR. It's pretty kludgey, but I'd be interested to see what happens. Hugin is still the right answer, tho ;-)